I hooked the TDML12DL today, and I am happy to report that it works great.
This accomplishes two things: first, the air compressor for the airbags will not go on in the middle of the night, it is now controlled by the ignition-on power. Second, the compressor will not rob the batteries from power on engine startup, as the start is now delayed for about a minute (adjustable from 0.1 to 102.3 seconds).
The relay does not look waterproof to me, so if you mount it outside, you may need some additional enclosure or something. I had mine mounted inside, with another relay outside.
TDML12DL can handle about 10 Amps by itself.